Unit 7 Percents NAME: GRADE: TEACHER: Ms. Schmidt

Transcription

1 Unit 7 Percents NAME: GRADE: TEACHER: Ms. Schmidt

2 Day 1 Classwork Understanding Percents The table to the right shows the ratio of people under 18 years of age to the total population for various states. 1) Name two states from the table that have ratios in which the second numbers are the same. 2) Of the two states you named in Exercise 1, which state has a greater ratio of people under 18 to total population? Explain. Hawaii Mississippi Utah 6 out of out of 8 out of 25 State Ratio of People Under 18 to Total Population Arkansas 1 out of 4 3) Describe how to determine which of the four states has the greater ratio of people under 18 to total population. Vocabulary: Ratio: Percent: Write each ratio as a percent: 1) According to the 2000 U.S. Census, 26 out of every people living in Illinois were younger than 18. 2) At a recent triathlon, 180 women competed for every women who competed ten years earlier. 3) During his baseball career, Babe Ruth had a base hit about 34 out of every times he came to bat. 4) In a recent year, 94.5 out of households in the United States had access to the Internet. 5) About 1 out of 5 luxury cars manufactured in the United States is white. 6) About 1 of travelers use scheduled buses ) In Finland, almost 4 out of 5 people have cell phone. 8) About 1 of the mammals in the world are bats. 4

3 Day 1 Classwork Writing Percents as Fractions: Paper 30% Plastic 24% Other Trash 35% Food and Yard Waste 11% Understanding Percents The circle graph shows an estimate of the percent of each type of trash in landfills. Write the percents for each of the following as a fraction in simplest form: Type of Trash Percent Fraction in Simplest Form Percent as a Decimal Paper Plastic Food and Yard Waste Other Trash Practice with Understanding Percents: I. Write each percent as a fraction in simplest form: a) 29% b) 43% c) 40% d) 125% e) 28% f) 64% g) 250% h) 4.5% II. Write each percent as a decimal: a) 50% b) 25% c).40% d) 75% e) 15% f) 2.8% g) 85% h) 1.25% III. Critical Thinking a) Which has a lesser value and why? 1 4 or 30% b) Explain how a student can receive an 86% on a test with 50 questions.

4 Day 1 Classwork Try These: Understanding Percents 1) Write the percent and the fraction in simplest form for the model shown at the left. Percent: Fraction: 2) Write a percent that is between 1 2 and 3 4 3) Circle the number that does not have the same value as the other three. Explain your reasoning % Write each ratio or fraction as a percent. 4) 25 out of 5) 3:20 6) 3.5 out of Write each percent as a fraction in simplest form: 7) 65% 8) 20.5% 9) 110% Write each percent as a decimal: 10) 45% 11) 2.8% 12) 80%

5 Day 2 Classwork Working with Mental Percents Vocabulary: Percent: Estimate: Mental Math in Percent Problems: Example: 10% of 50 Move the decimal point one place to the left. 10% of 50 is 5!! 1. 10% of % of % of % of % of % of 6,600 Example: 5% of 60 If 10% of 60 is 6, then 5% of 60 is 3! 7. 5% of % of % of % of 11. 5% of % of 1, What is 10% of 60? % of % of % of % of % of % of % of % of 80

6 Day 2 Classwork Working with Mental Percents Estimation: What if we aren t working with 5%, 10% or 20%? In these cases, ESTIMATE! Example: Find 22.8% of 162. Practice: 1. 32% of % of % of At a grocery store, four items cost $3.94, $7.11, $6.87, and $ Estimate the total cost of these items. 5. The Yankees had 57,435 fans at the stadium. Of those fans, 81% of them were actually rooting for the Yankees. Estimate how many fans were rooting for the Yankees. 6. Ella decides to buy a car for $28,945, a computer for $1,189 and a HDTV for $2,206. Estimate the total cost of Ella s purchases. 7. There are 1,289 students enrolled at Sequoya. 38% of the students are in seventh grade. Estimate how many students are seventh graders.

7 Day 2 Homework Working with Mental Percents What would you estimate the following to be? 1. $ % 3. 41% Determine the best estimate % of % of % of Joe had 119 catches this year. If 19% of his catches are touchdowns, about how many touchdowns does he have? 8. Maria took a test that had 50 questions. She got 78% of them correct. About how many questions were right? 9. Jessica went shopping for the holidays and purchased jeans for $45.75, a sweater for $36.20, and a hat and scarf for $ She had a 20% off coupon. Estimate how much she saved off her total cost. Review: 10) Solve: 11) Simplify: 12) Solve and Graph: (x 4) + 7x 15 x 1 4 x 5

8 Day 3 Classwork Deconstructing Percents Deconstructing percents or decimals is finding the decimal or percent that you will actually pay for the item. When would you add the percent or decimal Tax or Tip When would you subtract the percent or decimal Sale or Discount Examples: 7% Tax = 1.07 or 107% Examples: 40% Sale = 60% or % Tip = 1.2 or 120% 15% Discount = 85% or 0.85 Rewrite each as a final percent. Be sure to show the deconstruction. 1. Tax of 12% 7. 20% gratuity 2. Discount of 12% 3. Tip of 18% 4. on sale for 18% off 5. 25% markup 8. pay a fine of 30% 9. 5% rebate 10. the item depreciated 10% in value *11. 20% commission 6. 35% markdown A) Determine if the following represent tax/tip or discount. B) State the amount of the percent change. Be sure to show the deconstruction % % % % % % Write each decimal as a deconstructed percent A) Write each expression as a decimal. B) Determine if it represent tax/tip or discount. 22. x x 23. a 0.2a 24. y 0.086y 25. m + 0.3m

9 Day 3 Homework Deconstructing Percents A) Rewrite each percent as a Final equivalent tax/tip percent. Be sure to show the deconstruction. B) Rewrite each percent as a Final equivalent discount percent. Be sure to show the deconstruction % A) 122% B) 78% 2. 7% 3. 13% 4. 65% 5. % A) Rewrite each percent as a Final equivalent tax/tip DECIMAL. Be sure to show the deconstruction. B) Rewrite each percent as a Final equivalent discount DECIMAL. Be sure to show the deconstruction 6. 22% A) 1.22 B) % 8. 13% 9. 65% 10. % Solve the following using deconstructed percents or decimals 11. You have lunch at Chilli s and decide to leave a 20% tip, what is the final decimal that you will pay? 12. A Twilight DVD is 30% off the original price, what is the percent you pay for it? 13. If you pay 9% tax on a sweatshirt at Hollister, what is the decimal that you pay? 14. A coat is going on sale for 30% off, and you will have to pay 6% in tax, what is the final percent you will pay for the coat?

10 Day 4 Classwork Three Cases of Percents is of % OR part whole % Vocabulary: Percent Proportion: Example 1: The first type of problem is when the percent is given & the whole. (Find the part). Example: Find 80% of % of 150 is what number? 2. 75% of 60 is what number? Example 2: The second type of problem is when the percent is given & the part. (Find the whole). Example: 60 is 80% of what number? is 180% of what number? is 60% of what number? Example 3: The third type of problem is when the part and whole are given. (Find the percent). Example: 60 is what percent of 75? is what percent of 150? 8. What percent of 30 is 12?

11 Day 4 Classwork Three Cases of Percents is of % OR part whole % 9. Nick answered 90% of the questions on his math correctly. If he answered 45 of the questions correctly how many questions were on the test? 10. The Jets played 8 games. If they lost 2, and there were no ties, what percent of the games did they WIN? 11. Of the 200 bicycles at a vacation resort, 40 are NOT yet rented. a. What percent are not rented? b. What percent are rented? 12. There are 330 seventh graders at Sequoya Middle School. The number of seventh graders is 30% of the number of students enrolled in the school. How many students are enrolled at Sequoya? 13. Joe has 50 CD s. 28 are rap, 22 are rock. What percent of Joe s CD s are rock?

12 Day 4 Homework Three Cases of Percents is of % OR part whole % Directions: Set up a proportion or an equation and solve. Round your answer to the nearest tenth. 1. What percent of 30 is 12? is what percent of 250? 3. What is 0.7% of 45? is what percent of 250? 5. 20% of 88 is what number? is 98% of what number? 7. A hockey team won 6 games and lost 2. What percent of the games did they win? 8. James received a bonus that is 40% of the monthly salary. If his monthly salary is $800, how much was his bonus? 9. Of the 300 golf clubs Ray has at his miniature golf stand, 60 are being used. What percent of the golf clubs are not being used? 10. Simplify: ) Simplify: 2 (6x 12) 3

13 Day 5 Classwork Percent of Change Vocabulary: Percent of change: Percent of Increase: Percent of decrease: Percent of discount/markdown: Percent markup: Change Original % EXAMPLE: 1. In the US during the 20 th century, the average life expectancy increased from 50 to 75 years. Find the percent of increase. Steps: 1. Find the amount of increase (+). Change Original % 2. A shipment of seafood costs Red Lobster $850. The next shipment of the same quantity of seafood cost $782. What is the percent decrease in the cost? Step 1: Find the amount of decrease ( - ) % Change 2. changeoriginal= Original % 3. Your friend diets and goes from 125 pounds to 110 pounds. What was her percentage weight loss? Change a) Find the amount of decrease b) Original %

14 Day 5 Classwork Percent of Change 2. Eric bought a sweatshirt from Hollister for $30. If it originally cost $40, what was his percent of discount? (round to the nearest percent) 3. In last week s game, the basketball team scored 30 points. This week they scored 24 points. What percent of last week s score was the decrease? 4. Shannon is selling some embroidered jackets on a Web site. She wants to price the jackets 25% over her cost, which is $35. Find the selling price for a jacket. 5. At a supermarket, a certain item has increased from 75 cents per pound to 81 cents per pound. What is the percent markup in the cost of the item? 6. What is the markup rate on a $230 game system that sells for $345?

15 Day 5 Homework Percent of Change 1. Best Buy decreased the cost of a Sony flat screen monitor from $525 to $430. What is the percent of decrease? 2. Vinny swam 50 laps on Wednesday and 55 laps on Friday. The increase is what percent of Wednesday s laps? 3. Find the selling price for a $700 computer if the store has a 30% markup rate. 4. Write a percent of increase problem where the percent of increase is greater than %. 5. Jared and Sydney are solving the following problem. The price of a movie ticket rose from $5.75 to $6.25. What is the percent of increase for the price of a ticket? Who is correct? Explain. Jared Sydney % % Bicycle Bob rented 60 bikes on Saturday, and 180 on Sunday. a. What is the percent increase of bikes rented? b. What might account for the increase in rentals on Sunday?

16 Day 6 Classwork Percent Error Vocabulary: Relative Error: Percent Error: Relative Error Formula: measured actual actual Percent Error Formula: measured actual actual 1. Joshua uses his thermometer and measures to find the boiling point of ethyl alcohol to be 75 o C. He looks in a reference book and finds that the actual boiling point of ethyl alcohol is 80 o C. What is the relative error? What is his percent error? 2. The density of water is known to be 1.00 g/ml. Kayla measured and found the density of water to be g/ml. What is the relative error? What is her percent error? 3. The Handbook of Chemistry and Physics lists the actual density of a certain liquid to be g/ml. Taylor experimentally measures and finds this liquid to have a density of g/ml. The teacher allows up to +/- 0.5% error to make an A on the lab. Did Fred make an A? Prove your answer. 4. An object has an actual mass of 35.0 grams. On Anthony s balance, it measured to be grams. What is the percent error of his balance? 5. What is the percent error in using 3.14 as an approximation for π (which is )?

17 Day 6 Homework Percent Error Relative Error Formula: measured actual actual Percent Error Formula: measured actual actual 1) A carpenter measures the length of a board as 50.5 centimeters. The actual measure of the length was 50.1 centimeters. Find the relative error in the carpenter s measure to the nearest thousandth. 2) The actual length of the diagonal of a rectangle is 85. Sarah drew the same dimensional rectangle and measured the diagonal to be 87. Find, to the nearest hundredth, her relative error. 3) Eli bought new carpet for his living room. He measured the area of the living room to be square feet. The actual area was square feet. What is the relative error of the area to the nearest ten-thousandth? 4) A dairy sells milk in gallon (16 cups) containers. The containers are filled by machine and the amount of milk may vary slightly. A quality control employee selects a container at random and measures of the amount of milk as cups. Find the percent of error to the nearest tenth of a percent. 5) To calculate the area of her rectangular garden, Jill measured the length as 8 feet and the width to be 5 feet. The actual length of the garden is 8.2 feet by 4.7 feet. What is the percent of error in her area calculation to the nearest hundredth? (HINT: find the area of each first)